SO(9,1) invariant matrix formulation of supermembrane

TL;DR

This paper develops an $SO(9,1)$ invariant matrix formulation of the supermembrane in 11 dimensions, combining symmetry treatments and analyzing the superalgebra, including central charges.

Contribution

It introduces a novel $SO(9,1)$ invariant supermembrane formulation with explicit symmetry and polynomial Lagrangian, extending previous models and analyzing superalgebra charges.

Findings

The formulation includes terms not obtainable by naive dimensional reduction.

The Hamiltonian and supercharges are matrix regularized using standard procedures.

Only the two-form charge appears as a central charge in the superalgebra.

Abstract

An $SO(9,1)$ invariant formulation of an 11-dimensional supermembrane is presented by combining an $SO(10,1)$ invariant treatment of reparametrization symmetry with an $SO(9,1)$ invariant $\theta_{R} = 0$ gauge of $\kappa$-symmetry. The Lagrangian thus defined consists of polynomials in dynamical variables (up to quartic terms in $X^{\mu}$ and up to the eighth power in $\theta$), and reparametrization BRST symmetry is manifest. The area preserving diffeomorphism is consistently incorporated and the area preserving gauge symmetry is made explicit. The $SO(9,1)$ invariant theory contains terms which cannot be induced by a naive dimensional reduction of higher dimensional supersymmetric Yang-Mills theory. The $SO(9,1)$ invariant Hamiltonian and the generator of area preserving diffeomorphism together with the supercharge are matrix regularized by applying the standard procedure. As an application of the present formulation, we evaluate the possible central charges in superalgebra both in path integral and in canonical (Dirac) formalism, and we find only the two-form charge $[X^\mu, X^\nu]$.